- Hückel's rule
In

organic chemistry ,**Hückel's rule**estimates whether aplanar ringmolecule will havearomatic properties. The quantum mechanical basis for its formulation was first worked out by physical chemistErich Hückel in1931 . It was first expressed succinctly as the 4n+2 rule by von Doering in 1951. A cyclic ring molecule follows Hückel's rule when the number of its π electrons equals $4n\; +\; 2$ where $n$ is zero or any positiveinteger (although clearcut examples are really only established for values of n=0 up to about 6). Hückel's rule was based on calculations using theHückel method , although it can also be justified by considering aparticle in a ring system.Aromatic compounds are more stable than theoretically predicted by alkene hydrogenation data; the "extra" stability is due to the delocalized cloud of electrons, called resonance energy. Criteria for simple aromatics - (1) follow Huckel's rule, having 4n+2 electrons in the delocalized cloud, (2) are able to be planar and are cyclic, (3) every atom in the circle is able to participate in delocalizing the electrons by having a p orbital or an unshared pair of electrons.

**Refinement**Hückel's rule is not valid for many compounds containing more than three fused aromatic nuclei in a cyclic fashion.. For example,

pyrene contains 16 conjugated electrons (8 bonds), andcoronene contains 24 conjugated electrons (12 bonds). Both of these polycyclic molecules are aromatic even though they fail the 4n+2 rule.The

Hückel method andPariser-Parr-Pople method are a more precise means of estimating the properties of a π-system.**Three-Dimensional Rule**In 2000, chemists in

Germany formulated a rule to determine when afullerene would be aromatic. In particular, they found that if there were $2(n+1)^2$ πelectrons , then the fullerene would display aromatic properties. This follows from the fact that an aromatic fullerene must have fullicosahedral (or other appropriate) symmetry, so the molecular orbitals must be entirely filled. This is only possible if there are exactly $2(n+1)^2$ electrons, where $n$ is a nonnegative integer. In particular, for example,buckminsterfullerene , with 60 π electrons, is non-aromatic, since 60/2=30, which is not aperfect square .

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